Massey defines in [1]} a natural isomorphism giving the commutation of the vanishing cycles functor (considered as a functor \(\phi _f:D^b_c(U)\rightarrow D^b_c(U_0)\) ) with the Verdier duality \(\mathbb {D}\phi _f\simeq \phi _f\mathbb {D}\) . Consider the Cartesian diagram of closed subspaces:
\(\begin{tikzcd}U^{an}_0[dr,"q"] & &\\&\tilde{U}^{an}_0\cap \tilde{U}^{an}_\pi [r,"\hat{j}_\pi "][d,"\hat{j}_0"][dr,"m"] & \tilde{U}^{an}_0[d,"j_0"]\\&\tilde{U}^{an}_\pi [r,"j_\pi "] & U\end{tikzcd}\) 
